Category: Integration

Question Number 157175 by cortano last updated on 20/Oct/21 Commented by puissant last updated on 20/Oct/21 $$\mathrm{\Omega }=\frac{{\pi }^2}{4}$$ Answered by Mathspace last updated…

Question Number 91630 by Ar Brandon last updated on 02/May/20 $$\mathrm{show}\mathrm{that}$$$${\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\frac{\sin 2\mathrm{x}}{{(2+\cos 2\mathrm{x})}^2}\ln (1+{\mathrm{e}}^{\mathrm{x}})\mathrm{dx}$$$$=\frac{\pi }{16}-\frac{\pi \sqrt{3}}{36}$$ Commented by Ar Brandon…

Question Number 91619 by abdomathmax last updated on 02/May/20 $$calculate{\int }_2^{+\mathrm{\infty }}\frac{{(-1)}^{\left[2x\right]}}{x\left[x\right]-1}dx$$ Commented by mathmax by abdo last updated on 02/May/20 $$=\sum_{{n}=\mathrm{2}}…

Question Number 91620 by abdomathmax last updated on 02/May/20 $$letf\left(x\right)=2x-\sqrt{x-1}$$$$find\int \frac{f\left(x\right)}{f^{-1}\left(x\right)}dxand\int ln\left(\frac{f\left(x\right)}{f^{-1}\left(x\right)}\right)dx$$ Commented by mathmax by abdo last updated on 02/May/20…

Question Number 91611 by ar247 last updated on 01/May/20 $$findthevolumeoftheregion$$$$betweencurves(xy=4andx+y=5)$$$$revolvexaroundtheXaxis$$ Commented by john santu last updated on 02/May/20 $${vol}\:=\:\pi\:\int\underset{\mathrm{1}}…